基于Banach空间几何学的最佳逼近问题研究进展  

Research Progress of the Best Approximation Problems Based on Banach Space Geometry

作　　者：张子厚 周宇 刘春燕 刘瑞娟 ZHANG Zihou;ZHOU Yu;LIU Chunyan;LIU Ruijuan(School of Mathematics,Physics and Statistics,Shanghai University of Engineering Science,Shanghai,201620,P.R.China)

机构地区：[1]上海工程技术大学数理与统计学院,上海201620

出　　处：《数学进展》2020年第5期513-527,共15页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.11671252,11771278)。

摘　　要：本文从Banach空间几何学在逼近论中应用的视角,结合作者所做的一些工作,对最佳逼近问题中最佳逼近元的存在性、几乎存在性、最佳逼近问题的适定性及度量投影算子的连续性四方面问题近年来的研究进展作了系统介绍和综述,并提出一些开问题.From the perspective of the application of Banach space geometry in approximation theory,combined with some work done by the author,the paper systematically introduces and summarizes the research progress of the following four aspects—the existence and almost existence of the best approximation element,the well-posedness of the best approximation problem and the continuity of the metric projection operator in recent years.Some open problems are also put forward in this paper.

关 键 词：严格凸性 强凸性 H性质 自反性 最佳逼近元 近迫性 逼近紧性 度量投影 

分 类 号：O177.2[理学—数学] O174.41[理学—基础数学]